# Arturo ErdelyUniversidad Nacional Autónoma de México | UNAM · School of Higher Studies (F.E.S.) Acatlán

Arturo Erdely

Ph.D in Science (Statistics)

## About

39

Publications

6,463

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171

Citations

Introduction

Copula functions and its application for modeling dependent random variables

Additional affiliations

May 2010 - present

Education

February 2003 - January 2007

August 2000 - February 2003

October 1988 - November 1993

## Publications

Publications (39)

By applying Sklar's theorem to the Multivariate Bernoulli Distribution (MBD), it is proposed a framework that decouples the marginal distributions from the dependence structure, providing a clearer understanding of how binary variables interact. Explicit formulas are derived under the MBD using subcopulas to introduce dependence measures for intera...

In this work, a novel technique for efficient computation of bivariate empirical copulas and, by extension, non-parametrical copulas. The algorithm addresses discrete and finite equations, integrating mathematical-statistical components. It introduces two novel concepts: Propagation and Overlapping, to enhance computations and their comprehension d...

This report in PDF contains code in R and notes related to computational implementation of Joint stochastic simulation of petrophysical properties with elastic attributes based on parametric copula models

The spatial stochastic co-simulation method based on copulas is a general method that allows simulating variables with any type of dependency and probability distribution functions. This flexibility comes from the use of a copula model for the representation of the joint probability distribution function. The method has been mainly implemented thro...

A frequent task in exploratory data analysis consists in examining pairwise dependencies between data variables. Popular approaches include visualizing correlation or scatter plot matrices. However, both methods can be misleading. The former is primarily limited because it reports a single value for a pair of random variables. Furthermore, scatter...

A new methodology for the simulation of spatially distributed petrophysical properties conditioned by elastic attributes as secondary variables is presented. The method, namely Bernstein copula-based spatial cosimulation (BCSCS), is based on Bernstein copula for the estimation of the joint probability function and simulated annealing for the spatia...

Resumen En este artículo, se propone una metodología para un análisis estadístico de las estimaciones del conteo rápido institucional desde la perspectiva ideal de los resultados de los cómputos distritales de la elección de gobernador del Estado de México en 2017, particularmente en lo que atañe a aspectos como la precisión de las estimaciones, el...

An electoral quick count is a statistical procedure whose main objective is to obtain a relatively small but representative sample of all the polling stations in a certain election, and to measure the uncertainty about the final result before the total count of votes. A stratified sampling design is commonly preferred to reduce estimation variabili...

Se argumenta que el concepto de "empate técnico" en encuestas y conteos rápidos electorales no tiene fundamento probabilístico, y que en su lugar la incertidumbre asociada a dichos ejercicios estadísticos debiera expresarse en términos de una probabilidad de triunfo del candidato puntero. Palabras clave: empate técnico, encuesta electoral, conteo r...

It is argued that the concept of "technical tie" in electoral polls and quick counts has no probabilistic basis, and that instead the uncertainty associated with these statistical exercises should be expressed in terms of a probability of victory of the leading candidate. ----- Se argumenta que el concepto de "empate t\'ecnico" en encuestas y conte...

In many naturally fractured reservoirs, fractures play a crucial role in their flow and transport properties. An approach that has recently gained popularity for modeling fracture systems is the Discrete Fracture Network (DFN) model. This approach consists in applying a stochastic boolean simulation method, also known as object simulation method, w...

A novel Bernstein copula-based spatial stochastic co-simulation (BCSCS) method for petrophysical properties using seismic attributes as a secondary variable is presented. The method is fully nonparametric, and it has the advantages of not requiring linear dependence between variables. The methodology is illustrated in a case study from a marine res...

Most common parametric families of copulas are totally ordered, and in many cases they are also postively or negatively regression dependent and therefore they lead to monotone regression functions, which makes them not suitable for dependence relationships that imply or suggest a non-monotone regression function. In the present work it is proposed...

A dependence measure for arbitrary type pairs of random variables is proposed and analyzed, which in the particular case where both random variables are continuous turns out to be a concordance measure. Also, a sample version of the proposed dependence measure based on the empirical subcopula is provided.

The so-called risk diversification principle is analyzed, showing that its convenience depends on individual characteristics of the risks involved and the dependence relationship among them. ----- Se analiza el principio de diversificaci\'on de riesgos y se demuestra que no siempre resulta mejor que no diversificar, pues esto depende de caracter\'i...

Modeling the spatial distribution of petrophysical properties in the framework of reservoir characterization is a crucial and difficult task due to the lack of data and hence the degree of uncertainty associated with it. For this reason, in the last years a stochastic simulation approach for the spatial distribution of petrophysical properties has...

In this brief note we prove that linear B-spline copulas is not a new family of copulas since they are equivalent to checkerboard copulas, and discuss in particular how they are used to extend empirical subcopulas to copulas.

In this brief note we prove that linear B-spline copulas is not a new family of copulas since they are equivalent to checkerboard copulas, and discuss in particular how they are used to extend empirical subcopulas to copulas.

A statistical test based on the geometric mean is proposed to determine if a
predictive model should be rejected or not, when the quantity of interest is a
strictly positive continuous random variable. A simulation study is performed
to compare test power performance against an alternative procedure, and an
application to insurance claims reserving...

Statistical dependence between petrophysical properties in heterogeneous formations is usually nonlinear and complex; therefore, traditional statistical methods based on assumptions of linearity and normality are usually not appropriate. Copula based models have been previously applied to this kind of variables but it seems to be very restrictive t...

In this paper we study possible multivariate generalizations of construction of n-copulas with a given diagonal section. In the case of Archimedean n-copulas we prove that Frankʼs condition, which establishes when an Archimedean 2-copula is characterized by its diagonal section, can be extended to larger dimensions.

En este trabajo se presenta un método no paramétrico general de simulación estocástica conjunta de propiedades petrofísicas utilizando la cópula Bernstein. Este método consiste básicamente generar simulaciones estocásticas de una determinada propiedad petrofísica (variable primaria) modelando la dependencia empírica subyacente con otras propiedades...

In petrophysics, assessment of formation permeability is a complex and challenging problem that plays a key role in reservoir forecasts and optimal reservoir management. In heterogeneous carbonate reservoirs, permeability evaluation is commonly performed using permeability-porosity relationships, which often seem to be nonlinear and complex. Copula...

The statistical dependence between petrophysical properties (porosity, permeability, water saturation, etc.) in heterogeneous formations is usually nonlinear and complex; therefore, traditional statistical techniques based on assumptions of linearity are not appropriate for modeling these dependence relationships. Also, these methods may not reprod...

The statistical dependence between petrophysical properties (porosity, permeability, water saturation, etc.) is usually nonlinear and complex in heterogeneous formations, therefore, traditional statistical techniques, based on assumptions of linearity of the joint distribution function, are not appropriate for modeling these relationships, see Bala...

In petrophysics, assesment of formation permeability is a complex and challenging problem that plays a key role in reservoir forecasts and optimal reservoir management. In heterogeneous carbonate reservoirs, permeability evaluation is commonly performed using permeability-porosity relationships, which often seem to be nonlinear and complex. Copulas...

Assessment of rock formation permeability is a complicated and
challenging problem that plays a key role in oil reservoir modeling,
production forecast, and the optimal exploitation management. Generally,
permeability evaluation is performed using porosity-permeability
relationships obtained by integrated analysis of various petrophysical
measureme...

Based on the works by Klement and Mesiar (Comment Math Univ Carolinae 47:141–148, 2006) and Nelsen (Stat Pap 48:329–336, 2007)
on maximal asymmetry of copulas, we define and study the concept of tri-symmetry and we propose a simple statistic to test
symmetry of a bivariate copula, given a random sample of an absolutely continuous bivariate random v...

Assessment of rock formation permeability is a complicated and challenging problem that plays a key role in oil reservoir
modeling, production forecast, and the optimal exploitation management. Generally, permeability evaluation is performed using
porosity-permeability relationships obtained by integrated analysis of various petrophysical measureme...

Se presenta un modelo SIR (Susceptibles - Infectados - Recuperados) como un proceso estocástico a tiempo discreto que generaliza el modelo clásico de Reed-Frost.

[Spanish] Se presenta una introduccion a conceptos y resultados basicos sobre copulas, y su utilidad para estudiar y medir dependencia de variables aleatorias, como consecuencia del Teorema de Sklar (1959).

In this paper we study the problem of independence of two continuous random variables using the fact that there exists a unique
copula that characterizes independence, and that such copula is of Archimedean type. We use properties of the empirical diagonal
to build nonparametric independence tests for small samples, under the assumption that the un...

We analyze some properties of the empirical diagonal and we obtain its exact distribution under independence for the two and three-dimensional cases, but the ideas proposed in this paper can be carried out to higher dimensions. The results obtained are useful in designing a nonparametric test for independence, and therefore giving solution to an op...

In this paper we analyze some properties of the discrete copulas in terms of permutations.
We observe the connection between discrete copulas and the empirical copulas, and then we
analyze a statistic that indicates when the discrete copula is symmetric and obtain its main
statistical properties under independence. The results obtained are useful i...

A solution is given for the open problem about designing a test of statistical independence based on the assumptions that the copula in question is Archimedean and that its diagonal section is d(x)=x^2, posted in Alsina, Frank and Schweizer (2003) Problems on associative functions, Aequationes Math. 66, 128-140.

The problem of constructing copulas with a given diagonal section has been studied
by Sungur and Yang (1996) and Fredricks and Nelsen (1997a,b, 2002). The results
of Sungur and Yang are especially relevant because, among other results, they have
proven that an Archimedean copula is characterized by its diagonal section. The
results obtained by Fred...

About associative functions and archimedean copulas.